The big ones that really cross at least a few age brackets, have wide general recognition and probably aren't going anywhere in the near future (I may take some liberties with what I consider to be a franchise) in no particular order-
Star wars
James Bond
Lord of the rings
Sherlock Holmes
Batman
Superman
Spiderman
Mission Impossible
Mario
Zelda
Pokemon
Indiana Jones
Back to the Future
The Karate Kid
A Nightmare on Elm Street
Friday the 13th
Child's Play
It
Rambo
Rocky
Jurassic Park
The Matrix
The Terminator
Teenage Mutant Ninja Turtles
Transformers
The Simpsons
Barbie
GI Joe
He-Man/Masters of the universe
Mickey Mouse
Toy Story
Looney Tunes
King Kong
Godzilla
Planet of the Apes
Mad Max
The Muppets
The Godfather
Ghostbusters
Alien
Star Trek
Robocop
Frankenstein
Dracula
Tarzan
Conan the Barbarian
Jaws
Harry Potter
The Incredible Hulk
The Dollars Trilogy
Sesame Street
The Hannibal Lecter series
MASH
I think in general, most people have at least heard of these properties, would probably recognize at least a few of the main characters, objects, logos, memes, quotes, the theme song, etc. they've probably made some reference to them, and could give at least a vague explanation about what they're about or what the major themes are whether or not they've actually seen/read the source material
In general, I'm kind of counting a franchise as something that has had at least 3 major installments, iterations, episodes, series, remakes, reboots, etc. so a stand alone book, movie, etc. wouldn't count, nor would a book or movie and a sequel, a book and a movie adaptation, etc. A book, a movie adaptation, and a reboot movie would, a film trilogy would,a tv series would, a movie that's been rebooted/remade a couple times would.
Barbie feels like a weird one on this list to me, unlike GI Joe who's had pretty big movies and cartoons and such that make it pretty hard to argue that it's a franchise, most of Barbie's notoriety comes from the dolls themselves and I'd be kind of hesitant to label a line of toys as a franchise instead of a brand, sure there's been animated movies and video games and such, but none of them had really been particularly noteworthy. And I wouldn't feel quite right labeling, for example, Lego as a franchise despite having had pretty considerable success with movies and video games and such. But the character of Barbie, branding, marketing, etc. kind of puts her in the same league as Mickey mouse and I just felt like she belonged on the list.
Some of the classic characters - Frankenstein, Dracula, Sherlock Holmes, are arguably not really a franchise, there's not necessarily one company or person who owns their likeness and is marketing them, but they loom large enough in the public consciousness that I think they deserve to be mentioned in this list as well
I tried to keep this relatively universal, though I'm sure my biases as a cis straight white American millennial male showed through in places. There's a lot of franchises that form pillars of pop culture for specific demographics but not necessarily in general, and I tried to stay away from them, but a few of them just felt significant enough to me to warrant inclusion, in particular I kind of question how much general appeal He-Man has, for example, but I feel like if you say "He-Man" everyone has a mental image of the character seared into their brain (personally, I'm not sure I've ever even seen a whole episode of He-Man or really engaged with any masters of the universe media in general, but there he is in my brain and I don't really know how he got there)